DIURNAL AND SEMIDIURNAL OCEANIC TIDE VARIATIONS OF UT1, LOD/EARTH's ROTATION RATE DUE TO (IERS 1996 CONVENTIONS)

Oceanic tides cause diurnal and semidiurnal components in UT1, lenght-of-day D and Earth's rotation rate ω. Table here below report the model of the IERS 96 conventions. It includes 8 periodic components (4 diurnal terms, 4 semidiurnal terms) under the form:

ΔUT1 = Σ Fi sin ξi + Gi cos ξi

ΔD = Σ Fi' cos ξi + Gi' sin ξi

Δω = Σ Fi'" cos ξi + Gi" sin ξi

where ξi is integer linear combination of Delaunay arguments, GMST + π and constant phase :
ξi = a1 l + a2 l' + a3 D + a4 F + a5 ω + a6 (GMST +π) +φ0

The units are 10-4 s for UT1, 10-5 s for ΔD , and 10-14 rad/s for ω. 


        l   l'  F   D   ω GMST + π    φ0   PERIOD        ΔUT1           ΔD           Δω           
                                    (deg.) (hours)     Fi     Gi     Fi'   Gi'    Fi"   Gi"       
Q1     -1   0  -2   0  -2   1        -90   26.868     0.02   0.05   -1.4   2.8    1.2  -2.4
O1      0   0  -2   0  -2   1        -90   25.819     0.12   0.16   -7.1   9.4    6.0  -7.9
P1      0   0  -2   2  -2   1        -90   24.066     0.03   0.05   -1.8   3.2    1.5  -2.7
K1      0   0   0   0   0   1         90   23.935     0.09   0.18   -5.4  11.2    4.6  -9.4
N2     -1   0  -2   0  -2   2          0   12.658    -0.04  -0.02    4.5  -1.8   -3.8   1.6
M2      0   0  -2   0  -2   2          0   12.421    -0.16  -0.07   19.6  -8.7  -16.6   7.4
S2      0   0  -2   2  -2   2          0   12.000    -0.08   0.00    9.5  -0.5   -8.1   0.4
K2      0   0   0   0   0   2          0   11.967    -0.02   0.00    2.5  -0.5   -2.1   0.4

 
Delaunay arguments 
(IERS Conventions 2000, from Simon et al., 1994, Astron. Astrophys. 282, 663-683):
     
 Mean anomaly of the Moon :
   l = 134°.963 402 51 + 1 717 915 923.2178" t + 31".879 2 t2 + 0".051 635 t3 - 0".000 244 70 t4
 
 Mean anomaly of the Sun  : 
   l'= 357°.529 109 18 +   129 596 581.0481" t - 0".553 2 t2 -  0".000 136 t3 - 0".000 011 49 t4
 
 F = L - Ω  with L mean longitude of the Moon  
   F =  93°.272 090 62 + 1 739 527 262.8478" t - 12".751 2 t2 - 0".001 037 t3 + 0".000 004 17 t4
 
 Mean elongation of the Moon from the Sun :
   D = 297°.850 195 47 + 1 602 961 601.2090" t -  6".370 6 t2 + 0".006 593 t3 - 0".000 031 69 t4

 Mean longitude of the ascending node of the Moon :
   Ω = 125°.044 555 01  - 6 962 890.543 1" t + 7".472 2 t2 + 0".007 702 t3 - 0".000 059 39 t4

where t is measured un Julian Centuries of 36525 days of 86400 seconds of Dynamical Time since J2000.0.          

Rotation angle in arcseconds : Greenwich Mean Sidereal Time + 180°

   GMST + π = (67310.54841 + (876600d0*3600 + 8640184.812866) t 
             + 0.093104 t2 - 6.2 10-6 * t3 )*15 + 648000.0


where t is measured un Julian Centuries of 36525 days of 86400 seconds of Dynamical Time since J2000.0.